Channel shaping filter

ABSTRACT

A CHANNEL SHAPING FILTER FOR LOCATION BETWEEN THE MODULATOR AND THE DEMODULATOR OF A CHANNEL OF A DATA TRANSMISSION SYSTEM, THE FILTER BEING FORMED BY AT LEAST ONE TRANSVERSAL NETWORK OF THE KIND COMPRISING AT LEAST TWO TIME DELAY NETWORK CIRCUITS EACH HAVING AN INPUT AND AN OUTPUT AND CONNECTED TOGETHER IN SERIES SO AS TO FROM A CHAIN HAVING AN INPUT, WHICH CONSTITUTES THE NETWORK INPUT, AND AN OUTPUT AND A NUMBER OF INTERMEDIATE JUNCTIONS EACH FORMED WHERE THE OUTPUT OF ONE SAID CIRCUIT IS CONNECTED TO THE INPUT OF THE NEXT SUCCEEDING SAID CIRCUIT IN THE CHAIN, THE NETWORK ALSO INCLUDING A SEPARATE CORRESPONDING PICK-OFF RESISTANCE ASSOCIATED WITH AND CONNECTED TO EACH OF THE SAID CHAIN INPUT, THE SAID CHAIN OUTPUT AND THE SAID INTERMEDIATE JUNCTIONS SO AS TO PROVIDE IN RESPONSE TO AN INPUT SIGNAL APPEARING AT THE NETWORK INPUT, A NUMBER OF PICK-OFF SIGNALS EQUAL IN NUMBER TO THE NUMBER OF THE RESISTANCES, AND THE NETWORK ALSO INCLUDING MEANS FOR COMBINING THE PICK-OFF SIGNALS IN PREDETERMINED RELATIONSHIP TO PRODUCE A NETWORK OUTPUT SIGNAL, THE TIME DELAY CIRCUITS AND THE PICK-OFF RESISTANCES AND THE SAID COMBINING MEANS OF THE NETWORK BEING SELECTED TO PROVIDE A PRESELECTED RELATIONSHIP BETWEEN THE OUTPUT AND THE INPUT SIGNALS OF THE NETWORK.

Dec. 12, 1972 T, STARR ETAL 3,706,054

CHANNEL SHAPING FILTER Filed Nov. 6, 1970 4 Sheets-Sheet 1 FIG. /(0/FIG. /(b/ AM) Au) I r2 l l/ a 1 1 12 l 2 4 2 4 21'! F/G. 2(0) F/G. Z/b),T\ F (t) i NElGHBOUR|NG PULSE A l I I i -3 -g ?=o g'? i=0 1% 2 n n n nn n n n n n n TIMEU) INVENTORS ARTHUR T. STARR DAVID G. EDWARDS ATTORNEY Dec. 12, 1972 STARR ETAL CHANNEL SHAPING FILTER 4 Sheets-Sheet 5Filed Nov.

Dec. 12, 1972 A. T. STARR ETAL 3, ,0

CHANNEL SHAPING FILTER Filed Nov. 6, 1970 4 Sheets-Sheet 4 I I szcono IAIM) I LOBE i 1 I I A/ u 5 l i i i 3n fn v 9 f?" @"T 3* f 1 l Hebe): i35500:) (4'200) I g i 9=wT=2TrT 3 3 a i imam R i4/3R 4R is? :R' 128Rz7a,.s 27a 21s 278 L 250,!5 250 I L i RT L 1% FIG. 9/) FIG. 9(8) 0 OUTUnited States Patent 3,706,054 CHANNEL SHAPING FILTER Arthur T. Starr,New Barnet, and David G. Edwards,

Tonbridge Wells, England, assignors to Xerox Corporation, Stamford,Conn.

Filed Nov. 6, 1970, Ser. No. 87,547 Claims priority, application GreatBritain, Apr. 21, 1970,

9,040/ 70 Int. Cl. H04b 3/14 US. Cl. 333-28 R 6 Claims ABSTRACT OF THEDISCLOSURE A channel shaping filter for location between the modulatorand the demodulator of a channel of a data transmission system, thefilter being formed by at least one transversal network of the kindcomprising at least two time delay network circuits each having an inputand an output and connected together in series so as to form a chainhaving an input, which constitutes the network input, and an output anda number of intermediate junctions each formed where the output of onesaid circuit is connected to the input of the next succeeding saidcircuit in the chain, the network also including a separatecorresponding pick-01f resistance associated with and connected to eachof the said chain input, the said chain output and the said intermediatejunctions so as to provide in response to an input signal appearing atthe network input, a number of pick-ofl? signals equal in number to thenumber of the resistances, and the network also including means forcombining the pick-01f signals in predetermined relationship to producea network output signal, the time delay circuits and the pick-01fresistances and the said combining means of the network being selectedto provide a preselected relationship between the output and the inputsignals of the network.

This invention is concerned with improvements in or relating tochannel-shaping filters for use in data-transmission systems which areof the type (hereinafter referred to as the type specified) wherein thesystem has at least one channel arranged to receive an input signal inthe form of a train of pulse-form signals at a predetermined repetitionrate and representing the data, that signal being supplied to amodulator to produce a modulator output wherein each said pulse-formsignal is represented, according to a prearranged code, as a normalsinusoid or as an inverted sinusoid, in each case of a carrier wavehaving a frequency equal to the said repetition rate, or as asignal-less interval of duration equal to the period of that carrierwave, the modulator output being conveyed over a transmission link to ademodulator for reconstitution of the said input signal. The inventionis particularly, but not exclusively, applicable to the case where themodulator-demodulator system is of the vestigial-sideband type.

According to the invention, there is provided a channelshaping filterfor location between the modulator and the demodulator of a channel of adata-transmission system of the type specified, the filter being formedby at least one transversal network of the kind comprising at least twotime-delay network circuits each having an input and an output andconnected together in series so as to form a chain having an input,which constitutes the network input, and an output and a number ofintermediate junctions each formed where the output of one said circuitis connected to the input of the next succeeding said circuit in thechain, the network also including a separate corresponding pick-oifresistance associated with and connected to each of the said chaininput, the said chain output and the said intermediate junctions so asto provide, in response to an input signal appearing at the networkinput, a number of pick-off signals equal in number to the number of theresistances, and the network also including means for combining thepick-off signals in predetermined relationship to produce a networkoutput signal, the timedelay circuits and the pick-01f resistances andthe said combining means of the network being selected to provide apreselected relationship between the output and the input signals of thenetwork.

Preferably, the or at least one of the networks has an even number ofthe time-delay circuits arranged in pairs, the circuits of each pairhaving equal time-delays and bcing symmetrically located at oppositesides of that one said intermediate junction which is at the centre ofthe chain, the pick-01f resistances being so selected that the pick-01fsignals comprise a single pick-off signal from the said central oneintermediate junction and a number of pairs of pick-off signals for eachof which pairs the two signals are similar except in that one istime-delayed relatively to the other.

In one arrangement, the or at least one of the networks gas time-delaycircuits which have each the same timeclay.

The combining means may comprise, at least in part, the connection of atleast two of the pick-off signals to a common point, and/or maycomprise, at least in part, an inverting amplifier for reversing thepolarity of at least one of the pick-off signals.

The invention also includes a data-transmission system of the typespecified, at least one said channel of the system having, connectedbetween the modulator and the demodulator of that channel, achannel-shaping filter according to the invention.

Two examples of the invention will now be described with reference tothe accompanying drawings in which:

FIGS. 1(a) and 1(b) show amplitude-frequency response curves ofelectrical transmission systems;

FIGS. 2(a) and 2(b) show the electrical output signals delivered by thesystems of FIGS. 1(a) and 2(b) respectively, in response to an inputsignal in the form of a pulse of very small width;

FIG. 3 shows amplitude-frequency response curves applicable to the casewhere information is transmitted by means of an amplitude-modulatedcarrier wave;

FIG. 4 is a block diagram illustrating a type of datatransmissionsystems to which the invention is applicable;

FIG. 5 shows certain amplitude-frequency response curves applicable tothe invention;

FIG. 6 is a part-schematic circuit diagram of one form of transversalnetwork which may be employed according to the invention;

FIG. 7 is a circuit diagram of a time-delay network for use in thenetwork of FIG. 6;

FIG. 8 is an amplitude-frequency response curve illustrating theinvention, and

FIGS. 9(A), 9(B) and 10 are part-schematic circuit diagrams of exemplaryforms of transversal networks according to the invention.

If an electrical transmission system has, as shown in FIG. 1(a), anamplitude-frequency response A(w) which is level over the frequencybandwidth of (ti/21:) 0 to 11/2, then the output of that system, inresponse to a unitamplitude input signal in the form of a pulse of verysmall width, is a symmetrical oscillation of the form of the curve F (t)of FIG. 2(a), where The oscillation is of maximum unit amplitude at atime taken to be t= and is of zero amplitude at times etc.

Thus, if a succession of the pulses is transmitted over the system at arepetition rate of 1/11, there is zero intersymbol interference in thatneighboring pulses are distinguishable at the output of the system,since (FIG. 2(a)) the maximum of each oscillation corresponds to zeroamplitude of the next oscillation.

If information is to be transmitted over an electrical transmissionsystem, it is essential that such zero intersymbol interference exists:it does not exist for all such systems.

The fiat response of FIG. 1(a) is not achievable in practice: even if itwere, the setting-up of such a system would be very critical because ofthe slow decay of the oscillation of FIG. 2(a).

The electrical transmission system may, instead, be selected to have anamplitude-frequency response of the form of FIG. 1(b) wherein theresponse is unity over the frequency bandwidth 0 to 12/4, and thenfollows a cosine curve so that A(w) equals /2 and 0 respectively at thefrequencies 11/2 and 321/4. In such case, the output of the system, inresponse to the said unit-amplitude input signal, is the oscillation F0) of FIG. 2(b), where sin mrt mrt one of the two factors.

In the case where the electrical transmission system includes amplitudemodulation of a carrier wave, if the received baseband spectrum is ofthe form of FIG. 1(b), then the spectrum at the output of the modulatorwith carrier frequency (11) is as shown by the full line of FIG. 3. Ifthe vestigial lower sideband is chosen with a cosine roll-off about thecarrier frequency, as shown by the broken line in FIG. 3, then thespectrum is a full, raised cosine curve extending as shown between thefrequencies 11/4 and 511/4. This response curve will be denoted by A(w).

Thus, the spectrum of an output wave due to a single unit input pulseshould possess the distribution A (w) in the modulated condition. Whenthat pulse is very short, the system response should have the form A (w)because an impulse has a uniform frequency-spectrum. But if that pulseis not very short, then its spectrum must be allowed for.

FIG. 4 illustrates the form of one channel of a datatransmission systemto which the invention is applicable, the system employing amplitudemodulation (1, 0) or l, 1), carrier modulation, and vestigialsingle-sideband transmission. A source in the form of a pulse generator1 provides (as indicated at 2) an input signal in the form of a train ofpulses which may be either of the kind (1, 0), or of the kind (1, 1) andwhich are each of duration 1/12 second. The pulses are fed to the inputof a switched modulator 3 wherein they are arranged to so modulate acarrier wave of frequency (n) Hz., which is synchronized with the sourceof the pulses, as to produce complete, but possibly separated, cycles ofthe carrier wave at the output of the modulator 3, according to aprearranged code.

Thus, for example, the arrangement may be such that where (as indicatedat 2) the input signal has, during four consecutive periods, themagnitudes 1, (0 or 1), (0 or -1), and 1 respectively, the modulatoroutput is zero during the second and third of the periods butconstitutes, during each of the first and fourth periods, a completenormal sinusoid of the carrier wave (as indicated by the full lines at4). In a variant of this arrangement (as in our co-pending patentapplication Ser. No. 87,545, filed on Nov. 6, 1970), the arrangement isthe same except in that the modulator 3 is so arranged that eachalternate one of the sinusoids is inverted. In an alternative variant ofthe first-mentioned arrangement, the modulator output during each of thesaid second and third of the periods is not zero but comprises acomplete inverted sinusoid of the carrier wave (as indicated by thebroken lines at 4). Other, similar arrangements are also within thescope of the invention.

In the more general case, the pulse generator 1 may supply pulse-formsignals at the repetition rate (n), which signals may be of any shape,provided that the modulator 3 always yields full single sinusoids, asdescribed above.

The modulator output is then conveyed over a transmission link(indicated at 5) to a switched demodulator 6, a shapingvestigial-sideband filter 7 being interposed between the output of themodulator 3 and the input of the demodulator 6. The output signal fromthe demodulator 6 is passed through a low-pass filter 8 of which thefunction is to pass, without attenuation or phase distortion, waves of afrequency up to and a little beyond the frequency (12) Hz.

The filter 7 is conveniently located either at the modulator output orat the demodulator input; alternatively, it may in certain cases beformed in two portions which are located remote from one another.

Had the system input been in the form of very narrow pulses, then therequired characteristic of the filter 7 would have been A (w) of FIG. 3.The required characteristic for the actual arrangement will now bederived.

The spectrum of a single-cycle sinusoid is given by 1/21: =2 S111(Zarnt) sin wtdt 41rn sin (oi/27L) 41r n w where F is the sine wave, sin(Z-rnt) for one cycle only, i.e. between and It is convenient to choosea normalising factor such that A (w)=1 at the frequency w/21r=n. ThenSince, at the receiving end of the system, we require the spectraldistribution A (w), the filter '7 should therefore have thecharacteristic A (w)/A (w).

FIG. 5 includes plots of the functions A (w), A (w), l/A (w) and A (w)/A(w) against frequency (w/Zwr), for the particular case where n=2400 Hz.

It is in general difiicult to design and construct a filter 7 with therequired characteristic, but we have found simplified ways of doing thisin the present case.

In the first of the two methods to be described, it is shown how toderive two networks respectively with responses of the forms A (w) and1/A (w): these two networks will, when placed in tandem (e.g. asindicated by broken lines in FIG. 9, where is a buffer amplifier stage),yield the required response factor A (w)/A (w). In the second of the twomethods to be described, the network yields directly the requiredresponse factor.

FIRST METHOD Each of the methods makes use of at least one transversalnetwork of a particular kind (of which one example is shown in FIG. 6)..In the case of FIG. 6', the transversal network comprises four identicaldelay networks 11, 12, .13, and 14 each having input terminals 15, 16and output terminals 17, 18, the networks 11-14 being connected togetherin series, output to input, to form a chain.

Each of the networks l11-1'4 of FIG. 6 has the same time-delay T, sothat if a wave represented by e is supplied to the input of one of thosenetworks, there emerges at the output of that network a correspondingwave represented by e ie each of the networks has a response factor e-FIG. 7 shows one suitable form of delay network. The terminal 15 isconnected to the terminal 17 by way of three series-connectedinductances L L and L the inductances L and L being intercoupled and thethree inductances being bridged by a capacitance C The terminals 16 and18 are directly interconnected by a line which is connected, by Way of acapacitance C to the common point of the inductances L and L in FIG. 6,the input terminal 16 of the network 11, and the output terminal 18 ofthe network 14, are connected to earth. The chain of networks may thusbe regarded as having an input (aiforded by the terminal 15 of thenetwork 1r1, which terminal is connected to the input terminal 19 of thecomplete transversal network), an output (afforded by the terminal 17 ofthe network 14), and three intermediate junctions each formed where theoutput of one of the networks 11-13 is connected to the input of thenext succeeding network in the chain, the three intermediate junctionsbeing in this case afforded by the terminals 17 of the respectivenetworks 11-13.

The transversal network also includes a separate corresponding pick-ofiresistance associated with and connected to each of the said chaininput, the said chain output and the said intermediate junctions so asto provide, in response to an input signal appearing at the networkinput (terminal 19), a number of pick-01f signals equal in number to thenumber of the resistances. In the case of FIG. 6, these resistances areconstituted respectively by the resistances 24, 28, and 25, 26, 27, theremote ends of the resistances being shown as commoned by connection tothe output terminal 30 of the transversal network. In the idealized caseof FIG. 6, the resistance 26 is of magnitude R the resistances 25 and 27are of identical magnitude R and the resistances 24 and 28 are ofidentical magnitude R the resistances R R and R correspondingrespectively to conductances o 1 and 2- A suitable terminal impedance,in the form of a resistance R is connected in known manner between theterminals 17 and 18 of the network 14.

Thus, in FIG. 6, the output current wave (at the terminal 30, when 30 isconnected to a very low impedance) for unit input wave (at the terminal19) is the sum of the five pick-oif signals obtained respectively viathe five resistances 24 28, and is given by it being noted that thisresult is obtained by combining four of the five pick-oif signals inpairs (e.g. g eand g e of which the two signals are of equal amplitude(g but difier in that one is delayed relatively to the other.

The factor rjwzT may be ignored, since it represents only adistortionless delay of 2T. Then the transversal network of FIG. 6 hasthe response We require to choose T, g g and g such that A (w) has therequired form of A (w). Noting that'A is symmetrical about 6=wT=1r, wechoose T such that 0=1r at the frequency ail 21r 4 at which (FIGS. 3, 8)A (w) has its maximum value of unity. This gives We then choose g g andg such that A is equal to A at 0:0, 1r/3 and 21r/3 noting that A willthen have the correct values at 4T 51r 6:? E- and 21r We thus put A =0at 0 0, A =0 at 0: and A at 0:;

The resulting equations give The following table shows how close A (w)is to A (w):

The ratio of the resistances R =R =R is given by the ratio the negativesign indicating that those pick-off signals which are obtained via theresistances 25 and 27 (of re sistance R need to be inverted relativelyto the remaining pick-off signals.

In the case where (n), as referred to in connection with FIG. 4, isequal to 2400 bits/ second (as in FIG. 5), T=2/7200=278 microseconds,and the required network of response A (w)=A (w) may have the basic formshown in FIG. 9(A) wherein R represents the magnitude of a basicresistance and 35 represents an amplifier of current gain equal to(--1), of very low input impedance, and of high output impedance.

In practice, in certain cases the magnitudes and/or arrangement of thepick-oif resistances of FIG. 9(A) may have to be modified somewhat, ingenerally known manner and by simple experiment, in order to obtain therequired result. An example of such a modification is given in ourco-pending patent application Ser. No. 87,546, filed on Nov. 6, 1970.Such modification is necessitated because, whereas the above theoryassumes that, for each day of the delay networks 11-14, the associatedpick-01f resistances can be so chosen as not to significantly affect thevalues of the load and source impedances presented to those networks, inpractice however, convenient values of those resistances do not alwaysmeet this condition. In selecting such modified pick-off resistances,the basic principle mentioned above may be borne in mind, that therequired result can be obtained by combining four of the five pick-offsignals in pairs of which the two signals are of equal amplitude butditfer in that one is delayed relatively to the other.

We also require a further network with response factor 1/a (w) (shown inFIG. 5 This curve is roughly a cosine curve on a pedestal, with aminimum at a frequency of about 2000 Hz. We obtain the desired responseby means of a transversal network of the general kind described abovebut having only two of the identical delay networks and thus having aresponse of the form We choose T in this case, such that 9=wT=1r at thefrequency to =2000 HZ.

which gives T=i250 microseconds. We then choose g and g such that (as inFIG. 5) l/A =1.l8 at the frequency 1200 Hz. and 1/A =0.96 at thefrequency 2000 whence g =1.28 and g =0.16 and A 0) =1.28(1+0.25 cos wT)In this case, the ratio of the resistances R zR is given by the ratioand the required network may have the basic form shown in FIG. 9(B)wherein R represents the magnitude of a basic resistance, and R is theterminal resistance.

It is again to be understood that the circuit of FIG. 9(3) is of basicform and may in practice be modified in the general manner describedabove for the case of FIG. 9(A). Similar comments apply in the presentcase.

The complete filter is obtained by connecting the two networks of FIGS.9(A) and 9(B) in tandem, for example as indicated by the broken lines inFIG. 9, where 100 represents an amplifier, with a very low inputimpedance, which amplifies the current wave from point 37 and presentsit as a voltage wave with the correct source impedance to the input ofthe network of FIG. 9(B). It will be clear that, of the two parts of thefilter, FIGS. 9(A) and 9(B) respectively, one may be located at theoutput of the modulator 3 and the other at the input of the demodulator6.

SECOND METHOD We make small differences to the amplitudes and angles ofthe transversal network, of the form of FIG. 6, which has the response.

A (w) /3 [1% cos wT+ /2 cos 240T] which is nearly equal to A (w) Thesedifferences consist in perturbing slightly the conductances g g and gand the delay time T, such that the resulting network has a response ofthe form 5= 60S cos 2(1+d) e] where e has been written for QT, and wherea, b, c and d are to be small.

Noting that, with these assumptions,

cos (1+b)e cos e-be sin e and cos 2 (1+d)e,- cos 20-2de sin 20 we find,on ignoring products in (ab) and (cd), that A5=A3+V3 (--a cos a+%b0 sinli-l-c cos 26d0 sin 20) In order to fit A to the curve (A /A of FIG. 5,we choose, A =0 at 0=60 and at 0=300 (i.e. FIG. 5, at the frequencies600 Hz. and 3000 Hz. respectively). This gives We now choose to arrangethat the responses afforded by A at 0:120 and 6=240 (i.e. FIG. 5, at thefrequencies 1200 Hz. and 2400 Hz. respectively) shall be the correctfractions of the required response of A and 6=180 (i.e. FIG. 5, at thefrequency 1800 Hz.). Referring to FIG. 5, we therefore require that(1:0.226, b-=0.017, c=0.226, and d=0.0254

so that the required response is of the form 11 /3 (11.726 cosl.0l76+0.274 cos 2.0510) Since 0=wT=1r at the frequency 1800 Hz.(corresponding to n=2400), T=278 microseconds and thus cos 1.0170 andcos 2.0510 respectively require delays of 1.017 X 278:282 microsecondsand of 288 microseconds. The required network of response A =A /A isthus of the form shown in FIG. 10. It will be noted that the chain ofdelay networks comprises two pairs, 11' and 14, and 12 and 13', thenetworks of each pair having equal timedelays and being symmetricallylocated at opposite sides of that one side intermediate junction 40which is at the centre of the chain. If the resistance 26', the equalresistances 25' and 27, and the equal resistances 24' and 28', haveresistances which are respectively R R and R then R ':R :R =1:l.l6:7.3,R representing in FIG. 10 the magnitude of a basic resistance and 35'representing an amplifier similar to the amplifier 35.

The network of FIG. 10 will provide anti-phase components of about 0.10in the frequency bands between 0 and 300 Hz. and between 3300 and 3600Hz., but it is probable that the transmission link 5 (FIG. 4) willsuppress these components.

It is to be understood that the circuit of FIG. 10 is of basic form, andsimilar remarks apply here as above in the case of the circuit of FIG.9(A).

We claim: 1. A transversal filter for location between the modulator andthe demodulator of a channel of a data transmission system, comprising;

an even number of time delay circuits connected in seties to form achain having an input and an output,

separate pick-off resistive means connected to corresponding ones of thechain input and output, and the intermediate junctions between saidtime-day circuits to provide, in response to an input signal appearingat the network input, a number of pick-01f signals equal in number tothe number of the resistive means,

first means for combim'ng and inverting the polarity of the pick-oil?signals from those of the pick-01f resistive means connected to thejunctions at the outputs of the delay circuits located at the oddpositions in chain, and

second means for directly combining the pick-off signals from theremainder of pick-off resistive means and the output of said firstcombining and inverting means for providing an output signal of saidtransversal filter, wherein each of the respective pairs of said delaycircuits located at symmetrically opposite sides of the center junctionof the chain has an equal time delay and provides predetermined amountsof diflerent time delays relative to other pairs of the delay circuitsas a function of the base carrier fre quency of the transmission systemand the pick-off resistive means located symmetrically at the oppositesides of the center pick-off resistive means have a same resistancewhereby said transversal filter provides a preselected relationshipbetween the input and output thereof.

2. The filter according to claim 1 wherein said chain includes four timedelay circuits and five pick-oif resistive means comprised of a resistorR connected to the center junction, an inner pair of resistors R locatedsymmetrical- 1y on opposite sides of said center pick-off resistor R andouter pair R located outside of said inner pair of resistors, whereinthe value of said resistances are related in terms of their magnitude R:R :R =1:1.16:7.3.

3. The filter according to claim 2, wherein the values of the circuitelements of said time delay circuits, pick-oft resistors, and combiningmeans are so selected that said filter functions as a vestigial sideband filter in said data transmission system.

4. A transversal filter for location between the modulator and thedemodulator of a channel of a data transmission system, comprising;

first chain of an even number of time delay circuits connected in serieshaving an input and an output,

separate pick-0E resistive means connected to corresponding ones of saidfirst chain input and output, and the intermediate junctions betweensaid timedelay circuits to provide, in response to an input signalappearing at the network input, a number of pickoff signals equal innumber to the number of the resistive means,

first means for combining and inverting the polarity of the pick-offsignals from those of the pick-01f resistive means connected to thejunctions at the outputs of the delay circuits located at the oddpositions in the chain, and

second means for directly combining the pick-off signals from theremainder of pick-off resistive means and the output of said firstcombining means for providing an output signal of said first chain,

a second chain of even number of time delay circuits connected in serieswherein the input thereof is connectable to the output of said firstchain and the output is connectable to the demodulator of thetransmission system wherein the time delays introduced by 10 the delaycircuits of said second chain are different from the time delaysintroduced by the delay circuits of said first chain.

5. The filter according to claim 4 wherein said first chain includesfour time delay networks and five pick-off resistive means wherein twoouter pairs of resistive means connected to the input and output andintermediate junctions have resistances which are four times (4R) andfour third (4/3R) times the resistance R of the resistive meansconnected to the center junction, and wherein said second chain includesa pair of time delay networks and a pair of resistive means locatedsymmetrically on opposite sides of the center junction of the secondchain having eight times the resistance value of the pickotf resistivemeans connected to said center junction of the second chain.

6. The filter according to claim 5 wherein the values of the circuitelements of said time delay circuits, pick-off resistors, and combiningmeans are so selected that said filter functions as a vestigial sideband filter in said data transmission system.

References Cited UNITED STATES PATENTS 3,292,110 12/1966 Becker 333183,070,749 12/1962 Burns et a1 328177 3,001,137 9/1961 Kassel et a1 328383,537,038 10/1970 Rich 333- T 3,017,578 1/1962 Lundry 330-87 PAUL L.GENSLER, Primary Examiner U.S. c1. X.R.

